Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54

TL;DR

This paper provides an exact analysis of relaxation dynamics in the quantum cellular automaton Rule 54, demonstrating convergence to Gibbs states and non-equilibrium steady states, confirming generalized hydrodynamics predictions.

Contribution

It offers the first exact description of relaxation to a NESS in an interacting quantum system, validating generalized hydrodynamics for inhomogeneous quenches.

Findings

Finite subsystems relax to Gibbs states.

Inhomogeneous quenches lead to NESS as predicted.

First exact confirmation of generalized hydrodynamics in this context.

Abstract

We study the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 using a time-channel approach. We exhibit a family of (non-equilibrium) product states for which we are able to describe exactly the full relaxation dynamics. We use this to prove that finite subsystems relax to a one-parameter family of Gibbs states. We also consider inhomogeneous quenches. Specifically, we show that when the two halves of the system are prepared in two different solvable states, finite subsystems at finite distance from the centre eventually relax to the non-equilibrium steady state (NESS) predicted by generalised hydrodynamics. To the best of our knowledge, this is the first exact description of the relaxation to a NESS in an interacting system and, therefore, the first independent confirmation of generalised hydrodynamics for an inhomogeneous quench.